The Allied Control Council (ACC) which was meant to oversee the occupation governments of the four Allied occupation zones of Germany was only partly functional, and ceased to effectively exist in March 1948. The two initial problems were the French and the Soviets. The French wanted economic control of the Rhineland, the Ruhr and the Saar, and opposed the unification of Germany. The Soviets wanted $20 billion in reparations from Germany, and when the US refused to negotiate with $20 billion as the starting figure, they proceeded to loot their occupation zone to get what they could. The ACC operated by consensus, so all four occupying powers could veto any ACC decision.

The ACC stopped functioning when the Western Allies planned to introduce currency reforms (the Deutsche Mark). Planning began with the US and the British, and the French were willing to go along with it. The USSR was not, and in March 1948, the Soviet representative stopped attending ACC meetings, making a four-power consensus impossible (the ACC next met in 1971). Unable to introduce a Germany-wide currency reform, the Western Allies introduced the Deutsche Mark in their three zones in June 1948. The Soviet response was the Berlin Blockade. The Western Allies responded by setting up the Federal Republic of Germany (Bundesrepublik Deutschland, AKA West Germany) in May 1949. West Germany had its own government, but was not yet independent - it was still under the control of the Western Allies.

The Soviet Union was rather unhappy about establishment of West Germany, and responded by established an East German government in October 1949. East Germany was nominally a sovereign state from the beginning, but Soviet forces stayed in East Germany, and East Germany was in practice a Soviet puppet state.

The was the state of affairs when Stalin made his 1952 proposal for a unified Germany, with neutrality as the key condition. As a neutral state, not allowed to enter into any defensive alliances with other states, Germany would need its own army - Stalin did not propose disarmament, but instead re-armament. The West rejected enforce neutrality - a unified Germany would be free to ally with the West. Thus it stalled, and the proposal ended with the deaths of Stalin and Beria (Khrushchev was not willing to support such reunification of Germany).

Was this a "missed chance"? Nobody knows for sure - Stalin's motives were opaque. It is possible that the offer was sincere, since it would avoid 3/4 of Germany aligning with the West and 1/4 with the Soviet Union (and a well-looted 1/4 at that) - the West would lose more from a neutral Germany than the Soviets. It is also possible that Stalin expected non-agreement, and would have made sure that there was no agreement in more detailed negotiations - rejection of a neutral reunified Germany justified the integration of East Germany into the Soviet Bloc. One suspicion of the West German government is that negotiations were intended to force Western - and West German - recognition of the legitimacy of the East German government.

but totally changed its mind after that, what happened?

Stalin died, and Khrushchev thought that a Western orientation of a unified Germany would be the result, so the offer was no longer on the table.